Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952513559> ?p ?o ?g. }
- W2952513559 abstract "We consider the problem of computing an approximate banded solution of the continuous-time Lyapunov equation $underline{A}underline{X}+underline{X}underline{A}^{T}=underline{P}$, where the coefficient matrices $underline{A}$ and $underline{P}$ are large, symmetric banded matrices. The (sparsity) pattern of $underline{A}$ describes the interconnection structure of a large-scale interconnected system. Recently, it has been shown that the entries of the solution $underline{X}$ are spatially localized or decaying away from a banded pattern. We show that the decay of the entries of $underline{X}$ is faster if the condition number of $underline{A}$ is smaller. By exploiting the decay of entries of $underline{X}$, we develop two computationally efficient methods for approximating $underline{X}$ by a banded matrix. For a well-conditioned and sparse banded $underline{A}$, the computational and memory complexities of the methods scale linearly with the state dimension. We perform extensive numerical experiments that confirm this, and that demonstrate the effectiveness of the developed methods. The methods proposed in this paper can be generalized to (sparsity) patterns of $underline{A}$ and $underline{P}$ that are more general than banded matrices. The results of this paper open the possibility for developing computationally efficient methods for approximating the solution of the large-scale Riccati equation by a sparse matrix." @default.
- W2952513559 created "2019-06-27" @default.
- W2952513559 creator A5003504954 @default.
- W2952513559 creator A5075716603 @default.
- W2952513559 date "2014-08-18" @default.
- W2952513559 modified "2023-09-27" @default.
- W2952513559 title "Sparse solution of the Lyapunov equation for large-scale interconnected systems" @default.
- W2952513559 cites W105839681 @default.
- W2952513559 cites W1506342804 @default.
- W2952513559 cites W1506690472 @default.
- W2952513559 cites W1514337951 @default.
- W2952513559 cites W1527992869 @default.
- W2952513559 cites W1551892507 @default.
- W2952513559 cites W1575737617 @default.
- W2952513559 cites W1609259884 @default.
- W2952513559 cites W1798474452 @default.
- W2952513559 cites W1969729070 @default.
- W2952513559 cites W1971942712 @default.
- W2952513559 cites W1974617506 @default.
- W2952513559 cites W1974637237 @default.
- W2952513559 cites W1977106787 @default.
- W2952513559 cites W1986652366 @default.
- W2952513559 cites W1993079101 @default.
- W2952513559 cites W2000255607 @default.
- W2952513559 cites W2001840567 @default.
- W2952513559 cites W2010315317 @default.
- W2952513559 cites W2016075148 @default.
- W2952513559 cites W2022704310 @default.
- W2952513559 cites W2026502086 @default.
- W2952513559 cites W2032894172 @default.
- W2952513559 cites W2035234197 @default.
- W2952513559 cites W2038535655 @default.
- W2952513559 cites W2043153343 @default.
- W2952513559 cites W2058273413 @default.
- W2952513559 cites W2059998776 @default.
- W2952513559 cites W2073998620 @default.
- W2952513559 cites W2078311192 @default.
- W2952513559 cites W2081647150 @default.
- W2952513559 cites W2082559624 @default.
- W2952513559 cites W2083643510 @default.
- W2952513559 cites W2088666624 @default.
- W2952513559 cites W2089301577 @default.
- W2952513559 cites W2091272557 @default.
- W2952513559 cites W2093875902 @default.
- W2952513559 cites W2094014020 @default.
- W2952513559 cites W2095170086 @default.
- W2952513559 cites W2095276381 @default.
- W2952513559 cites W2099629311 @default.
- W2952513559 cites W2104192126 @default.
- W2952513559 cites W2104359570 @default.
- W2952513559 cites W2104744926 @default.
- W2952513559 cites W2111684543 @default.
- W2952513559 cites W2111836897 @default.
- W2952513559 cites W2117354031 @default.
- W2952513559 cites W2124287091 @default.
- W2952513559 cites W2131275217 @default.
- W2952513559 cites W2133703348 @default.
- W2952513559 cites W2136598296 @default.
- W2952513559 cites W2137006204 @default.
- W2952513559 cites W2158983145 @default.
- W2952513559 cites W2169328438 @default.
- W2952513559 cites W2595142274 @default.
- W2952513559 cites W269260623 @default.
- W2952513559 cites W2798766386 @default.
- W2952513559 cites W2950730153 @default.
- W2952513559 cites W2952062910 @default.
- W2952513559 cites W2952822950 @default.
- W2952513559 cites W3102961917 @default.
- W2952513559 cites W50720323 @default.
- W2952513559 hasPublicationYear "2014" @default.
- W2952513559 type Work @default.
- W2952513559 sameAs 2952513559 @default.
- W2952513559 citedByCount "1" @default.
- W2952513559 countsByYear W29525135592015 @default.
- W2952513559 crossrefType "posted-content" @default.
- W2952513559 hasAuthorship W2952513559A5003504954 @default.
- W2952513559 hasAuthorship W2952513559A5075716603 @default.
- W2952513559 hasConcept C106487976 @default.
- W2952513559 hasConcept C11413529 @default.
- W2952513559 hasConcept C121332964 @default.
- W2952513559 hasConcept C158622935 @default.
- W2952513559 hasConcept C159985019 @default.
- W2952513559 hasConcept C163716315 @default.
- W2952513559 hasConcept C192562407 @default.
- W2952513559 hasConcept C202444582 @default.
- W2952513559 hasConcept C2778755073 @default.
- W2952513559 hasConcept C28826006 @default.
- W2952513559 hasConcept C33676613 @default.
- W2952513559 hasConcept C33923547 @default.
- W2952513559 hasConcept C41008148 @default.
- W2952513559 hasConcept C48103436 @default.
- W2952513559 hasConcept C56372850 @default.
- W2952513559 hasConcept C60640748 @default.
- W2952513559 hasConcept C62520636 @default.
- W2952513559 hasConceptScore W2952513559C106487976 @default.
- W2952513559 hasConceptScore W2952513559C11413529 @default.
- W2952513559 hasConceptScore W2952513559C121332964 @default.
- W2952513559 hasConceptScore W2952513559C158622935 @default.
- W2952513559 hasConceptScore W2952513559C159985019 @default.
- W2952513559 hasConceptScore W2952513559C163716315 @default.